When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$,
Conformal Prediction (CP) is a methodology that allows to estimate a confidence
set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of
the data is exchangeable. CP sets have guaranteed coverage for any finite
population size $n$. While appealing, the computation of such a set turns out
to be infeasible in general, e.g. when the unknown variable $y_{n+1}$ is
continuous. The bottleneck is that it is based on a procedure that readjusts a
prediction model on data where we replace the unknown target by all its
possible values in order to select the most probable one. This requires
computing an infinite number of models, which often makes it intractable. In
this paper, we combine CP techniques with classical algorithmic stability
bounds to derive a prediction set computable with a single model fit. We
demonstrate that our proposed confidence set does not lose any coverage
guarantees while avoiding the need for data splitting as currently done in the
literature. We provide some numerical experiments to illustrate the tightness
of our estimation when the sample size is sufficiently large, on both synthetic
and real datasets.

本论文将 CP 技术与经典算法稳定性界限相结合，提出了一种置信区间集合，可用单一模型拟合计算，并证明了该方法能够保证精度，避免了数据分割的需求，成功解决了传统方法无法处理连续未知变量 y_n+1 的瓶颈问题。

稳定的共形预测集

Stable Conformal Prediction Sets

We present a novel model architecture which leverages deep learning tools to
perform exact Bayesian inference on sets of high dimensional, complex
observations. Our model is provably exchangeable, meaning that the joint
distribution over observations is invariant under permutation: this property
lies at the heart of Bayesian inference. The model does not require variational
approximations to train, and new samples can be generated conditional on
previous samples, with cost linear in the size of the conditioning set. The
advantages of our architecture are demonstrated on learning tasks that require
generalisation from short observed sequences while modelling sequence
variability, such as conditional image generation, few-shot learning, and
anomaly detection.

该论文提出了一种新型的模型架构，利用深度学习工具对高维、复杂观测集进行精确贝叶斯推理。这一模型的特点是可交换性，不需要使用变分逼近来训练，并且可以有条件地生成新样本，其优点在于它可用于需要从短观察序列中进行广义学习的任务，同时对序列的变化进行建模，例如条件图像生成、少样本学习和异常检测。